1. A more eloquent or refined way of saying "shit".
2. Sometimes a stronger or more emphasized way of saying "shit": "really shit".

To understand the slightly paradoxical difference note that the word "shite" is usually said in a grimmer and lower tone than the word "shit", which is sharper to say. You can really tear into the word "shite" when you're using it as an insult as in the second example, the word "shit" ends more suddenly. However generally "shite" is not as offensive to say as "shit".